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arXiv 2307.05073cs.LO
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知识-wh 与错误信念敏感性:一项逻辑研究(扩展摘要)

Knowledge-wh and False Belief Sensitivity: A Logical Study (An Extended Abstract)

Yuanzhe Yang

AI总结:

本文通过引入四个捆绑算子并对相应逻辑进行公理化与比较,系统研究了知识-wh 在提及-某些知识、提及-某些真信念及其错误信念敏感性等不同解释下的逻辑差异与共性。

摘要:

在认知逻辑中,处理知识-wh 的一种方式是将其解释为某种提及-某些知识(MS-knowledge)。但哲学家和语言学家对这种解释的充分性和必要性都提出了挑战:一些人认为,知识-wh 除了提及-某些知识之外,还具有对错误信念的敏感性(FS);另一些人则认为,知识-wh 可能只蕴含提及-某些真信念(MS-true belief)。在本文中,我们对所有这些不同解释进行了逻辑研究。我们运用捆绑算子技术,引入四个不同的捆绑算子:$[\mathsf{tB}^\mathtt{MS}]^x ϕ:= \exists x (\mathsf{[B]} ϕ\wedge ϕ)$,$[\mathsf{tB}^\mathtt{MS}_\mathtt{FS}]^x ϕ:= \exists x (\mathsf{[B]} ϕ\wedge ϕ) \wedge \forall x (\mathsf{[B]} ϕ\to ϕ)$,$[\mathsf{K}^\mathtt{MS}]^x ϕ:= \exists x \mathsf{[K]} ϕ$ 和 $[\mathsf{K}^\mathtt{MS}_\mathtt{FS}]^x ϕ:= \exists x \mathsf{[K]} ϕ\wedge \forall x (\mathsf{[B]} ϕ\to ϕ)$,它们分别刻画了提及-某些真信念、带错误信念敏感性的提及-某些真信念、提及-某些知识以及带错误信念敏感性的提及-某些知识这些概念。我们对四个逻辑进行了公理化,这些逻辑将上述算子(以及 $\mathsf{[K]}$)作为 $S4.2$-常域模型类上的原始模态,并比较所得逻辑中的推理模式,以展示知识-wh 的四种解释彼此之间的差异以及它们的共同之处。

英文摘要:

In epistemic logic, a way to deal with knowledge-wh is to interpret them as a kind of mention-some knowledge (MS-knowledge). But philosophers and linguists have challenged both the sufficiency and necessity of such an account: some argue that knowledge-wh has, in addition to MS-knowledge, also a sensitivity to false belief (FS); others argue that knowledge-wh might only imply mention-some true belief (MS-true belief). In this paper, we offer a logical study for all these different accounts. We apply the technique of bundled operators, and introduce four different bundled operators: $[\mathsf{tB}^\mathtt{MS}]^x ϕ:= \exists x (\mathsf{[B]} ϕ\wedge ϕ)$, $[\mathsf{tB}^\mathtt{MS}_\mathtt{FS}]^x ϕ:= \exists x (\mathsf{[B]} ϕ\wedge ϕ) \wedge \forall x (\mathsf{[B]} ϕ\to ϕ)$, $[\mathsf{K}^\mathtt{MS}]^x ϕ:= \exists x \mathsf{[K]} ϕ$ and $[\mathsf{K}^\mathtt{MS}_\mathtt{FS}]^x ϕ:= \exists x \mathsf{[K]} ϕ\wedge \forall x (\mathsf{[B]} ϕ\to ϕ)$, which characterize the notions of MS-true belief, MS-true belief with FS, MS-knowledge and MS-knowledge with FS respectively. We axiomatize the four logics which take the above operators (as well as $\mathsf{[K]}$) as primitive modalities on the class of $S4.2$-constant-domain models, and compare the patterns of reasoning in the obtained logics, in order to show how the four accounts of knowledge-wh differ from each other, as well as what they have in common.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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